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Ch5 Data Mining Classification: Alternative Techniques

Ch5 Data Mining Classification: Alternative Techniques. Rule-Based Classifier. Classify records by using a collection of “if…then…” rules Rule: ( Condition )  y where Condition is a conjunctions of attributes y is the class label LHS : rule antecedent or condition

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Ch5 Data Mining Classification: Alternative Techniques

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  1. Ch5 Data Mining Classification: Alternative Techniques

  2. Rule-Based Classifier • Classify records by using a collection of “if…then…” rules • Rule: (Condition)  y • where • Condition is a conjunctions of attributes • y is the class label • LHS: rule antecedent or condition • RHS: rule consequent • Examples of classification rules: • (Blood Type=Warm)  (Lay Eggs=Yes)  Birds • (Taxable Income < 50K)  (Refund=Yes)  Evade=No

  3. R1: (Give Birth = no)  (Can Fly = yes)  Birds R2: (Give Birth = no)  (Live in Water = yes)  Fishes R3: (Give Birth = yes)  (Blood Type = warm)  Mammals R4: (Give Birth = no)  (Can Fly = no)  Reptiles R5: (Live in Water = sometimes)  Amphibians Rule-based Classifier (Example)

  4. A rule rcovers an instance x if the attributes of the instance satisfy the condition of the rule Application of Rule-Based Classifier R1: (Give Birth = no)  (Can Fly = yes)  Birds R2: (Give Birth = no)  (Live in Water = yes)  Fishes R3: (Give Birth = yes)  (Blood Type = warm)  Mammals R4: (Give Birth = no)  (Can Fly = no)  Reptiles R5: (Live in Water = sometimes)  Amphibians The rule R1 covers a hawk => Bird The rule R3 covers the grizzly bear => Mammal

  5. Rule Coverage and Accuracy • Coverage of a rule: • Fraction of records that satisfy the antecedent of a rule • Accuracy of a rule: • Fraction of records that satisfy both the antecedent and consequent of a rule (Status=Single)  No Coverage = 40%, Accuracy = 50%

  6. How does Rule-based Classifier Work? R1: (Give Birth = no)  (Can Fly = yes)  Birds R2: (Give Birth = no)  (Live in Water = yes)  Fishes R3: (Give Birth = yes)  (Blood Type = warm)  Mammals R4: (Give Birth = no)  (Can Fly = no)  Reptiles R5: (Live in Water = sometimes)  Amphibians A lemur triggers rule R3, so it is classified as a mammal A turtle triggers both R4 and R5 A dogfish shark triggers none of the rules

  7. Characteristics of Rule-Based Classifier • Mutually exclusive rules • Classifier contains mutually exclusive rules if the rules are independent of each other • Every record is covered by at most one rule • Exhaustive(无遗漏的、穷尽的) rules • Classifier has exhaustive coverage if it accounts for every possible combination of attribute values • Each record is covered by at least one rule

  8. From Decision Trees To Rules Rules are mutually exclusive and exhaustive Rule set contains as much information as the tree

  9. Rules Can Be Simplified Initial Rule: (Refund=No)  (Status=Married)  No Simplified Rule: (Status=Married)  No

  10. Effect of Rule Simplification • Rules are no longer mutually exclusive • A record may trigger more than one rule • Solution? • Ordered rule set(有序规则) • Unordered rule set(无序规则) • 采用投票策略,把每条被触发的后件看作是对相应类的一次投票,然后计票确定测试记录的类标号; • 在某些情况下,投票可以用规则的准确率加权; • 利:不易受由于选择不当的规则而产生错误的影响;不必维护规则的顺序,建立模型的开销也相对较小; • 弊:测试记录的属性要与规则集中的每一条规则的前件作比较,所以对测试记录进行分类是一件很繁重的任务。 • Rules are no longer exhaustive • A record may not trigger any rules • Solution? • Use a default class {} y

  11. Rules are ranked in descending order according to their priority(按优先级降序排列) 优先级的定义有多种方法:基于准确率、覆盖率、总描述长度或规则的产生顺序 有序的规则集也成为决策表( decision list) When a test record is presented to the classifier It is assigned to the class label of the highest ranked rule(排序最高的规则) it has triggered If none of the rules fired, it is assigned to the default class Ordered Rule Set R1: (Give Birth = no)  (Can Fly = yes)  Birds R2: (Give Birth = no)  (Live in Water = yes)  Fishes R3: (Give Birth = yes)  (Blood Type = warm)  Mammals R4: (Give Birth = no)  (Can Fly = no)  Reptiles R5: (Live in Water = sometimes)  Amphibians

  12. Rule-based ordering Individual rules are ranked based on their quality:依据规则质量的某种度量对规则排序,该方案确保每一个测试记录都是由覆盖它的“最好的”规则来分类 该方案的潜在缺点是排在越低的规则越难解释,因为每条规则都假设所有排在它前面的规则不成立 Class-based ordering Rules that belong to the same class appear together 质量较差的规则可能因为某个类的优先级较高排在前面而被触发,从而导致高质量规则被忽略。 Rule Ordering Schemes

  13. Building Classification Rules • Direct Method: • Extract rules directly from data • e.g.: RIPPER, CN2, Holte’s 1R • Indirect Method: • Extract rules from other classification models (e.g. decision trees, neural networks, etc). • e.g: C4.5rules

  14. Direct Method: Sequential Covering • Start from an empty rule • Grow a rule using the Learn-One-Rule function • Remove training records covered by the rule • Repeat Step (2) and (3) until stopping criterion is met 1. 令E是训练记录,A是属性-值对的集合{(Aj, vj)} 2. 令Y0是类的有序集{y1, y1, …, yk} 3. 令R={}是初始规则列表 4. for 每个类yY0-{yk} do 5. while 终止条件不满足 do 6. r Learn-one-rule(E, A, y) 7. 从E中删除被r覆盖的训练记录 8. 追加r到规则列表尾部:R R v r 9. end while 10. end for 11. 把默认规则{ }  yk插入到规则列表R尾部

  15. Example of Sequential Covering

  16. Example of Sequential Covering…

  17. Aspects of Sequential Covering • Rule Growing • Instance Elimination • Rule Evaluation • Stopping Criterion • Rule Pruning

  18. Rule Growing • Two common strategies • 先建立一个初始规则r: { }  y (质量很差, 覆盖所有样本) • 加入新的合取项提高规则的质量。探查所有可能的候选,并贪心地选择下一个合取项。 • 继续该过程,直至满足终止条件为止 • 可以随机选择一个正例作为规则增长的初始种子 • 求精步,通过删除规则的一个合取项,使其覆盖更多的正例来泛化规则。 • 继续该过程,直至满足终止条件为止

  19. Rule Growing (Examples) • CN2 Algorithm: • Start from an empty conjunct: {} • Add conjuncts that minimizes the entropy measure: {A}, {A,B}, … • Determine the rule consequent by taking majority class of instances covered by the rule • RIPPER Algorithm: • Start from an empty rule: {} => class • Add conjuncts that maximizes FOIL’s information gain measure: • R0: {} => class (initial rule) • R1: {A} => class (rule after adding conjunct) • Gain(R0, R1) = t [ log (p1/(p1+n1)) – log (p0/(p0 + n0)) ] • where t: number of positive instances covered by both R0 and R1 p0: number of positive instances covered by R0 n0: number of negative instances covered by R0 p1: number of positive instances covered by R1 n1: number of negative instances covered by R1

  20. Instance Elimination • Why do we need to eliminate instances? • Otherwise, the next rule is identical to previous rule • Why do we remove positive instances? • Ensure that the next rule is different • Why do we remove negative instances? • Prevent underestimating accuracy of rule • Compare rules R2 and R3 in the diagram

  21. Rule Evaluation • Statistical test • For example, compute the following likelihood ratio statistic: • Where k is the number of classes, is the observed frequency of class i examples that are covered by the rule, and is the expected frequency of a rule that makes random predictions. • Some explanation: compare the given rule with rule that makes random predictions. A large R value suggests that the number of correct predictions make by the rule is significantly large.

  22. Rule Evaluation • Statistical test • For example. • Consider a training set that contains 60 positive examples and 100 negative examples. • Rule1: covers 50 positive examples and 5 negative examples • Rule2: covers 2 positive examples and no negative examples • Rule1 covers 55 examples, the expected frequency for the positive class is e1 = 55*60/160 = 20.625, while the expected frequency for the negative class is e2 = 55*100/160 = 34.375

  23. Metrics: Accuracy Laplace M-estimate Rule Evaluation n : Number of instances covered by rule nc : Number of positive instances covered by rule k : Number of classes p : Prior probability of positive instances

  24. Stopping Criterion and Rule Pruning • Stopping criterion • Compute the gain • If gain is not significant, discard the new rule • Rule Pruning • Similar to post-pruning of decision trees • Reduced Error Pruning: • Remove one of the conjuncts in the rule • Compare error rate on validation set before and after pruning • If error improves, prune the conjunct

  25. Summary of Direct Method • Grow a single rule • Remove Instances from rule • Prune the rule (if necessary) • Add rule to Current Rule Set • Repeat

  26. Direct Method: RIPPER • For 2-class problem, choose one of the classes as positive class, and the other as negative class • Learn rules for positive class • Negative class will be default class • For multi-class problem • Order the classes according to increasing class prevalence (fraction of instances that belong to a particular class) • Learn the rule set for smallest class first, treat the rest as negative class • Repeat with next smallest class as positive class

  27. Direct Method: RIPPER • Growing a rule: • Start from empty rule • Add conjuncts as long as they improve FOIL’s information gain • Stop when rule no longer covers negative examples • Prune the rule immediately using incremental reduced error pruning • Measure for pruning: v = (p-n)/(p+n) • p: number of positive examples covered by the rule in the validation set • n: number of negative examples covered by the rule in the validation set • Pruning method: delete any final sequence of conditions that maximizes v

  28. Direct Method: RIPPER • Building a Rule Set: • Use sequential covering algorithm • Finds the best rule that covers the current set of positive examples • Eliminate both positive and negative examples covered by the rule • Each time a rule is added to the rule set, compute the new description length • stop adding new rules when the new description length is d bits longer than the smallest description length obtained so far

  29. Direct Method: RIPPER • Optimize the rule set: • For each rule r in the rule set R • Consider 2 alternative rules: • Replacement rule (r*): grow new rule from scratch • Revised rule(r’): add conjuncts to extend the rule r • Compare the rule set for r against the rule set for r* and r’ • Choose rule set that minimizes MDL principle • Repeat rule generation and rule optimization for the remaining positive examples

  30. Indirect Methods

  31. Indirect Method: C4.5rules • Extract rules from an unpruned decision tree • For each rule, r: A  y, • consider an alternative rule r’: A’  y where A’ is obtained by removing one of the conjuncts in A • Compare the pessimistic error rate for r against all r’s • Prune if one of the r’s has lower pessimistic error rate • Repeat until we can no longer improve generalization error

  32. Indirect Method: C4.5rules • Instead of ordering the rules, order subsets of rules (class ordering) • Each subset is a collection of rules with the same rule consequent (class) • Compute description length of each subset • Description length = L(error) + g L(model) • L(error) is the number of bits needed to encode the misclassified examples, L(model) is the number of bits needed to encode the model • g is a parameter that takes into account the presence of redundant attributes in a rule set(default value = 0.5) Recall the regression problem and classification problem: Regularization can prevent over-fitting, why? SVM is the most popular classifier, why? • The class that has the smallest description length is given the highest priority(Occam's Razor) • Occam’s Razor: It is a principle urging one to select among competing hypotheses that which makes the fewest assumptions

  33. Example

  34. C4.5 versus C4.5rules versus RIPPER C4.5rules: (Give Birth=No, Can Fly=Yes)  Birds (Give Birth=No, Live in Water=Yes)  Fishes (Give Birth=Yes)  Mammals (Give Birth=No, Can Fly=No, Live in Water=No)  Reptiles ( )  Amphibians RIPPER: (Live in Water=Yes)  Fishes (Have Legs=No)  Reptiles (Give Birth=No, Can Fly=No, Live In Water=No)  Reptiles (Can Fly=Yes,Give Birth=No)  Birds ()  Mammals

  35. C4.5 versus C4.5rules versus RIPPER C4.5 and C4.5rules: RIPPER:

  36. Advantages of Rule-Based Classifiers • As highly expressive as decision trees • Easy to interpret • Easy to generate • Can classify new instances rapidly • Performance comparable to decision trees

  37. Instance-Based Classifiers • Store the training records • Use training records to predict the class label of unseen cases

  38. Instance Based Classifiers • Examples: • Rote-learner • Memorizes entire training data and performs classification only if attributes of record match one of the training examples exactly • Nearest neighbor • Uses k “closest” points (nearest neighbors) for performing classification

  39. Compute Distance Test Record Training Records Choose k of the “nearest” records Nearest Neighbor Classifiers • Basic idea: • If it walks like a duck, quacks like a duck, then it’s probably a duck

  40. Nearest-Neighbor Classifiers • Requires three things • The set of stored records • Distance Metric to compute distance between records • The value of k, the number of nearest neighbors to retrieve • To classify an unknown record: • Compute distance to other training records • Identify k nearest neighbors • Use class labels of nearest neighbors to determine the class label of unknown record (e.g., by taking majority vote)

  41. Definition of Nearest Neighbor K-nearest neighbors of a record x are data points that have the k smallest distance to x

  42. 1 nearest-neighbor Voronoi Diagram

  43. Nearest Neighbor Classification • Compute distance between two points: • Euclidean distance • Determine the class from nearest neighbor list • take the majority vote of class labels among the k-nearest neighbors • Weigh the vote according to distance • weight factor, w = 1/d2

  44. Nearest Neighbor Classification… • Choosing the value of k: • If k is too small, sensitive to noise points • If k is too large, neighborhood may include points from other classes

  45. Nearest Neighbor Classification… • Scaling issues • Attributes may have to be scaled to prevent distance measures from being dominated by one of the attributes • Example: • height of a person may vary from 1.5m to 1.8m • weight of a person may vary from 90lb to 300lb • income of a person may vary from $10K to $1M

  46. Nearest Neighbor Classification… • Problem with Euclidean measure: • High dimensional data • curse of dimensionality • Can produce counter-intuitive results 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 0 0 0 0 0 0 0 0 0 vs 0 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 1 d = 1.4142 d = 1.4142 • Solution: Normalize the vectors to unit length

  47. Nearest neighbor Classification… • k-NN classifiers are lazy learners • It does not build models explicitly • Unlike eager learners such as decision tree induction and rule-based systems • Classifying unknown records are relatively expensive

  48. Example: PEBLS • PEBLS: Parallel Examplar-Based Learning System (Cost & Salzberg) • Works with both continuous and nominal features • For nominal features, distance between two nominal values is computed using modified value difference metric (MVDM) • Each record is assigned a weight factor • Number of nearest neighbor, k = 1

  49. Example: PEBLS Distance between nominal attribute values: d(Single,Married) = | 2/4 – 0/4 | + | 2/4 – 4/4 | = 1 d(Single,Divorced) = | 2/4 – 1/2 | + | 2/4 – 1/2 | = 0 d(Married,Divorced) = | 0/4 – 1/2 | + | 4/4 – 1/2 | = 1 d(Refund=Yes,Refund=No) = | 0/3 – 3/7 | + | 3/3 – 4/7 | = 6/7

  50. Example: PEBLS Distance between record X and record Y: where: wX 1 if X makes accurate prediction most of the time wX> 1 if X is not reliable for making predictions

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